everything.study
2.180

Biomolecular Feedback Systems

3-0-9 units · Undergraduate

Comprehensive introduction to mathematical modeling, dynamic analysis, and control of cellular biomolecular processes. Emphasizes design approaches for sophisticated biomolecular networks that are robust to the environment, both in bacterial and mammalian cells. Provides a review of biology concepts and detailed description of classical and novel mechanisms to regulate gene expression. Presents how to use these mechanisms to design feedback and feedforward control architectures. Covers basic enabling technologies from synthetic biology, engineering principles for designing biological functions, modular design techniques, and host-circuit interaction. Students taking graduate version complete additional assignments.

Spring 2015

Topics

  • Introduction: Overview of the course, biology and basic biological processes, and modeling.
  • Modeling techniques, chemical reactions and ordinary differentials equations (ODEs), reduced order models for common binding reactions.
  • Modeling transcription and translation: Chemical reactions and ODEs (full mechanistic models and reduced models).
  • Modeling transcriptional regulation: Chemical reactions and ODEs (emphasis on reduced models), examples.
  • Modeling post transcriptional regulation: Allosteric modification, covalent modification, ultrasensitivity, mitogen-activated protein kinases (MAPK) cascades.
  • Dynamic behavior: Stability and analysis near equilibria, nullcline analysis, linearization techniques, frequency response, examples.
  • Design principles for robustness: Sensitivity analysis to parameter perturbations, examples.
  • Design principles for robustness: Adaptation and disturbance rejection through integral feedback and feedforward loops, high gain feedback examples.
  • Design principles for limit cycles: Systems in two dimensions (2D), examples.
  • Design principles for limit cycles: Systems in nD, examples, bifurcation analysis, examples.
  • Model reduction through separation of time scales, examples.
  • Stochastic behavior: Master equation, Stochastic Simulation Algorithm (SSA) by Gillespie, examples.
  • Stochastic behavior: Langevin equation, examples.
  • Circuit design: Autorepressed systems, robustness, sensitivity, power spectra, dynamics.
  • Toggle switches, engineered memory, repressilator and the realization of loop oscillators.
  • Activator-repressor clock, incoherent feedforward motifs to control plasmid copy number.
  • Implementation of adaptation through methylation, chemotaxis circuit.
  • Interconnecting circuits: Retroactivity and examples, transcriptional circuits.
  • Retroactivity in signal transduction circuits.
  • Gene circuits: Equivalent input and output retroactivities, Thevenin’s theorem.
  • Insulation devices: Principle of functioning and design based on phosphorylation.
  • Insulation devices: Designs based on time scale separation and realizations with phosphotransfer cascades.
  • Insulation devices: Designs based on protease-feedback.
  • Design examples: Multi-module circuits, input output impedance (retroactivity) matching.
  • Design tradeoffs: Competition for gene expression machinery and isocosts.
  • Project presentations.

Readings

Prerequisites & course information

Same subject as 20.180[J] Subject meets with 2.18[J] , 20.418[J] Prereq: Biology (GIR) , 18.03 , or permission of instructor U (Spring) 3-0-9 units

Sources